Geometry of Spectral Curves and All Order Dispersive Integrable System
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Geometry of Spectral Curves and All Order Dispersive Integrable System
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| Creator |
Borot, G.
Eynard, B. |
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| Description |
We propose a definition for a Tau function and a spinor kernel (closely related to Baker-Akhiezer functions), where times parametrize slow (of order 1/N) deformations of an algebraic plane curve. This definition consists of a formal asymptotic series in powers of 1/N, where the coefficients involve theta functions whose phase is linear in N and therefore features generically fast oscillations when N is large. The large N limit of this construction coincides with the algebro-geometric solutions of the multi-KP equation, but where the underlying algebraic curve evolves according to Whitham equations. We check that our conjectural Tau function satisfies Hirota equations to the first two orders, and we conjecture that they hold to all orders. The Hirota equations are equivalent to a self-replication property for the spinor kernel. We analyze its consequences, namely the possibility of reconstructing order by order in 1/N an isomonodromic problem given by a Lax pair, and the relation between ''correlators'', the tau function and the spinor kernel. This construction is one more step towards a unified framework relating integrable hierarchies, topological recursion and enumerative geometry.
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| Date |
2019-02-19T18:22:25Z
2019-02-19T18:22:25Z 2012 |
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| Type |
Article
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| Identifier |
Geometry of Spectral Curves and All Order Dispersive Integrable System / G. Borot, B. Eynard // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 81 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 14H70; 14H42; 30Fxx DOI: http://dx.doi.org/10.3842/SIGMA.2012.100 http://dspace.nbuv.gov.ua/handle/123456789/149186 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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